Null hypothesis significance testing (NHST) is the most widely accepted and frequently used approach to statistical inference in quantitative communication research. NHST, however, is highly controversial, and several serious problems with the approach have been identified. This paper reviews NHST and the controversy surrounding it. Commonly recognized problems include a sensitivity to sample size, the null is usually literally false, unacceptable Type II error rates, and misunderstanding and abuse. Problems associated with the conditional nature of NHST and the failure to distinguish statistical hypotheses from substantive hypotheses are emphasized. Recommended solutions and alternatives are addressed in a companion article.